IE 360 Statistical Forecasting and Time
Series
Solar Power Forecasting Project Report
Instructor: Mustafa Gökçe Baydoğan
Project Group 28:
Melis Tuncer 2019402156
Kaan Ertan 2019402087
Sude Filiz 2021402273
Introduction:
The problem at hand depicts a real-life forecasting problem that involves many collinear
variables. The aim is to provide accurate predictions for hourly solar power production
of the Edikli Solar Power Plant in Niğde/Türkiye. Providing accurate predictions is
essential for real-life market operations since electricity pricing and capacity planning
will rely heavily on production forecasts. In the context of solar energy, it is impossible to
deliberately increase production without directly increasing the physical solar panel
capacity (eg: by improving panel power generation capacity, increasing the number of
panels, increasing panel maintenance, etc.). Therefore, the power generated in a day
depends completely on the incoming solar energy absorbed by the panels and
transformed into electrical energy. Since the solar energy plant has such a naturally
determined production amount, it is vital to predict the production beforehand for a more
advantageous pricing policy.
For the prediction of solar energy production beforehand, the best approach is to
construct a model that takes meteorological variables as inputs. Meteorological
variables have a direct effect on the incoming solar energy on the Earth’s surface,
thereby having an indirect effect on the solar power generated by the plant. This way,
the model can predict solar power generation using these observable parameters at
hand. Before moving on with our specific approach, it is fruitful to examine our variables
for a better understanding of the problem.
Descriptive Analysis of the Given Data & Variables:
For each variable whose data was given, we first analyzed the variable and its meaning
in our framework. Then we moved forward with their data visualization and the analysis
of their respective effects on the solar power production. For this, we utilized the ggplot
package in R. The following are the results of this analysis:
The Overall Plot of Our Production Data
(notice that both the seasonal nature of solar power production and the maximum solar
power production are clearly seen)
The Autocorrelation Function Plot of Our Production Data
The Partial Autocorrelation Function Plot of Our Production Data
DSWRF_surface: This variable is the “Downward Shortwave Radiation Flux on
Surface”, which is an estimate of the total shortwave radiation that reaches the Earth’s
surface. Its computation includes both the albedo (the fraction of light that is reflected by
Earth) and atmospheric composition of Earth. DSWRF significantly impacts the
production output of solar power plants, since when the flux is high solar panels receive
more sunlight and generate more electricity. During the days with low flux (due to clouds
or atmospheric conditions), plants generate much less electricity. However, it is vital to
note that this variable is strongly correlated to the atmospheric variables and therefore
there may be multicollinearity between those variables and this.
It is seen in the correlation table that DSWRF_surface variables of different location
groups all have positive correlation (seen in the 2. row, around 0.45) with production,
DLWRF_surface: This variable is the "Downward Longwave Radiation Flux on
Surface". Its difference from DSWRF is that DLWRF has a longer wavelength and it is
the solar-based radiation that is emitted back from Earth’s surface. In this sense, it
doesn’t contribute too much to the solar panels’ energy production directly. However,
since solar panels lose heat by this means, a higher DLWRF means that solar panels
will be colder early in the morning and it will take longer for them to heat up and this
slightly effects their efficiency.
In the correlation table we see that the DLWRF_surface variables of different location
groups have slightly positive correlation (around 0.08) with solar power production
USWRF_top_of_atmosphere: This variable is the “Upward Shortwave Radiation Flux
at the Top of the Atmosphere”, and represents the amount of shortwave solar radiation
reflected back into space from the top of the atmosphere. This flux is influenced by
factors such as cloud cover and atmospheric conditions. Changes in this can affect the
amount of solar radiation reaching the Earth's surface, and therefore the solar energy
production.
In the correlation table we see that the USWRF_top_of_atmosphere variables of
different location groups have slightly positive correlation (around 0.1) with production
USWRF_surface: This is the “Upward Shortwave Radiation Flux at the Earth's surface”,
and this variable shows the amount of shortwave solar radiation reflected by the Earth's
surface. Surface conditions such as the surface being land or water, vegetation, and
surface color all affect this variable. But since we are focusing on solar panel surfaces,
we can only use this variable to understand the flux intensity and therefore the incoming
solar energy. High values of USWRF_surface indicate more solar radiation hitting and
being reflected by the surface.
It is clear that the USWRF_surface variables of different location groups have positive
correlation (around 0.35) with production
TCDC_low.cloud.layer, TCDC_middle.cloud.layer, TCDC_high.cloud.layer,
TCDC_entire.atmosphere: These are the total cloud cover percentages for different
types of clouds. Although evaluating the entire atmosphere as a whole is easier and
yields less collinear results, it is important to note the differences of cloud types. Clouds
are classified according to their altitude in the atmosphere: low, middle, high. Low
clouds can significantly reduce solar radiation reaching the Earth's surface by blocking
direct sunlight. Moreover, they diffuse sunlight but do so unevenly over the surface. So
they may lead to a less uniform flux on solar panels, which may decrease efficiency.
Middle clouds cannot completely block sunlight like low clouds, but they still can reduce
solar flux by scattering, reflecting, and absorbing sunlight. Additionally, the presence of
middle clouds often indicate changing weather conditions, which can lead to further
changes in solar power generation either for the better or for worse. Lastly, high clouds
are thin clouds that can only block a limited amount of sunlight. However, they can still
reduce solar flux by scattering and diffusing sunlight. Similar to middle clouds, high
clouds may also indicate approaching weather systems. Their difference is that high
clouds often indicate weather changes in a longer term, and can be useful for long term
weather forecasting.
We see that the TCDC_entire.atmosphere variables of different location groups have
negative correlation (around -0.37) with production
CSNOW_surface: This is a categorical variable for the existence of snow. When the
solar panels are covered with snow, they cannot function until they are cleared off the
snow. Since the solar panels might get covered by snow in winter, it is important to
include this scenario in a model.
TMP_surface: This is the surface level temperature. Temperatures do not directly affect
solar power production, but are useful for representing seasonality. Since both the
surface temperatures and solar power generation are positively correlated to the sun
light exposure, this may be beneficial to model the seasonal differences in the sun light
exposure (due to both weather conditions and the Earth’s tilted axis resulting in different
day lengths). Moreover it is known that high temperatures affect the solar panels and
decrease their efficiency.
TMP_surface variables of different location groups have positive correlation
(around 0.53) with solar power production
Summary of Our Approach:
Our approach involved several steps and methodologies to ensure the reliability and
accuracy of our predictions.
We began by preparing the data in Python, transforming it into a wide format and
removing zero-production hours. Initial regression analyses indicated room for
improvement, leading us to switch to R for further analysis, where we examined ACF
and PACF plots to identify seasonal patterns and long-term dependencies. To enhance
model interpretability and accuracy, we applied Lasso regressions to select significant
variables.First, we performed Lasso regression on the original set of variables. Next, we
expanded the model by incorporating both the original and weighted variables. Lastly,
we employed a more stringent Lasso regression with a higher penalty parameter to
further refine the variable selection. Consequently, we transitioned to ARIMA models,
grouping the data by hour and updating the models daily with the most recent
information. Differencing techniques were used to remove trends and achieve
stationarity. After developing ARIMA models for each hour, we combined the results for
overall performance evaluation and attempted to create a unified ARIMA model using
the entire dataset.
Literature:
Our literature research was focused on 3 fields: understanding the general relationship
between atmospheric events and solar power generation, understanding the provided
variables and their meteorological foundations, and understanding methods to convert
this relationship into a forecasting model.
Solar power depends directly on factors such as the intensity and angle of the incoming
sunlight. The atmospheric conditions have a critical direct effect on the incoming
sunlight, so the provided variables have an indirect relationship with the solar power
generation since they work as an indicator of the incoming sunlight rather than a di rect
measure of it. For instance, the cloud cover parameters are definitely important for our
model, yet they do not have a direct impact on the power generation. Instead, they
affect the solar power production via their effect of filtering the incoming sunlight to the
Earth’s surface. This concept applies to the other parameters as well, in the sense that
our parameters merely reflect the changes in the incoming solar energy level, thus
helping us to understand and predict the solar power generation. This makes it
important to understand these parameters.
Of course, at the end of the day, we construct our model by examining and learning
from the past data. But understanding the climatological background is a must in order
to ensure that our model makes sense not only in reference to the data at hand, but
also in reference to the meteorological phenomena in the nature. For this, we examined
some key literature for meteorology and climatology by Adams & Lambert (2006) as
well as by Desonie (2012).
In order to construct a good model that learns from the data and provides accurate
forecasts, we benefitted mostly from the methods and frameworks that we have studied
in our course. In addition to these, we benefitted from time series modelling resources
such as Montgomery et al. (2008) and Hyndman & Athanasopoulos (2018). These
helped us to research for the best possible data cleaning and forecast making
strategies, and helped us to troubleshoot our mistakes on the way to the best solution.
Approach
Data Preparation Using Python:
At first, we used Python to transform the data into a wide format and eliminate duplicate
entries. Subsequently, we identified the hours when the production value was zero and
eliminated them from our model because they were unnecessary to our analysis. Hours
with zero production values were 0, 1, 2, 3, 4, 19, 20, 21, 22, and 23. We performed
regression analysis on the filtered_data that we obtained. The resulting R-squared value
was 0.629. Given that this value was exceedingly high, we continued to weight the
variables based on their 1/p values. We then conducted two regression analyses: one
with only the 10 weighted variables and one with 260 variables which includes both the
original and weighted variables. In both cases, the R-squared value was greater than
desirable. In our fourth approach, we conducted a series of individual regressions for
each variable, resulting ten different regression models. The primary goal of this
approach was to find out which location would be significant if we regression with that
seperate variable. However, the outcomes from this approach were suboptimal, yielding
no significant discoveries.
Following the implementation of these approaches in Python, we switched to R for
further analysis. After importing the necessary libraries in R, we examined the ACF plot
of our data.
Autocorrelation plot of time series data ‘production’
The ACF plot of the time series shows strong seasonal patterns with significant
autocorrelations at regular intervals, approximately every 12 lags. Furthermore the
gradual decay in autocorrelation over several lags indicates long-term dependencies in
the series, implying that implying that production levels fluctuate seasonally as well as
follow stable trends.
Then, we used the ggpairs function to examine the relationship between hour and
production.
R code snippet used to generate the plot depicting the relationship between hour and
production.
Pairwise plot examining the relationship between hour and production
In the lower left plot, we looked at the hours when production was highest. Since we do
not observe a linear relationship between time and production, we cannot take time as a
predictor. We transformed hour to -(hour-12)^2. By doing so, we ensure that the new
hour column has a linear relationship with production and it will have higher values
when it is close to 12, as expected.
After that, we utilized the ggplot function to visualize the relationship between date and
production.
Code snippet used to generate the plot depicting the relationship between date and
production at all hours
ggplot examining the relationship between hour and production
We notice that there is a maximum production level of approximately 10 in general
based on the ggplot. Consequently, we included the maximum production level for the
previous three days as a second variable for maximum production.
Regression with all variables:
Subsequently, we import and prepare the test data covering the period from February
1st to May 15th. For testing, we prepared the test data similarly, removed any missing
values, and used the model to predict solar power production. Negative predictions
were replaced with zero since production cannot be negative. We developed a time
series linear regression model utilizing all available variables, establishing this as our
baseline. As a result of our test, we found the adjusted R-squared to be 0.7393, which is
quite high.
We calculated the residuals (differences between actual and predicted values) and
plotted the actual and predicted values over time using ggplot, showing how well the
model's predictions matched the actual production values. Also, we plot the
autocorrelation function.
Residuals plot (top), ACF of residuals (bottom left), and histogram with density plot of
residuals (bottom right) for the regression model with all variables
Residual is the difference between an observed value and the value predicted by a
model.In our residuals plot there are periods where residuals are consistently above or
below zero, it might indicate that the model has not fully captured some underlying
patterns or seasonality in the data.
Also the ACF plot should ideally show no significant autocorrelations if the residuals are
purely random. Significant spikes at certain lags indicate that there is still some
autocorrelation left in the residuals, suggesting that the model might be missing some
temporal dependencies.
Although the residuals' histogram suggests they are roughly normally distributed, further
statistical tests could provide a more definitive conclusion. Additionally, we applied the
Ljung-Box test, a statistical test used to determine whether there is significant
autocorrelation in a time series' residuals, indicating whether the residuals are
independently distributed.
Actual vs. Predicted Production Values
In the Ljung-Box Test, the null hypothesis (H0) is that the residuals are independently
distributed (no autocorrelation), while the alternative hypothesis (H1) is that the
residuals are not independently distributed (there is autocorrelation). Since our p-value
is much smaller than 0.05, we reject the null hypothesis. This indicates that there is
significant autocorrelation in the residuals of our model, suggesting that the model has
not fully captured all the temporal dependencies in the data.
Using the ‘accu’ function, we evaluated the performance metrics of the baseline linear
model.
Summary of performance metrics for the baseline linear model
This baseline model provided a reasonable starting point, but results suggested room
for improvement. So we continued with lasso regression.
Lasso Regression:
Lasso regression is an analysis technique that selects variables and applies
regularization to improve the statistical model's interpretability and prediction accuracy.
We tried to eliminate least effective variables using lasso regression. We used
‘cv.glmnet’ function to perform cross-validation and identify the optimal lambda value.
Cross-validated Mean Squared Error (MSE) vs. Log(lambda)
The minimum mean squared error (MSE) is typically found when the model complexity
is at its highest, meaning more predictors are included. To avoid overfitting, we use a
lambda value within one standard deviation of the minimum MSE.
Afterwards, we continued with the 178 variables we selected with lasso regression.
First Approach : Linear Regression with Lasso Variables + Transformed Hour:
In this approach, we began by preparing our data, which involved transforming the
'hour' variable.
We applied Lasso regression to select the most significant variables from our dataset,
and then included the transformed hour variable in our feature set. Using these
features, we fitted a linear regression model which we called Lasso(1sd)-LM.
To evaluate the model, we analyzed the residuals through various plots, such as
residuals over time, the autocorrelation function (ACF) of residuals, and a histogram of
residuals with a density plot.
Residuals plot , ACF of residuals , and histogram with density plot of residuals for the
first approach.
ACF plot examining the relationship between hour and production
PACF plot with a maximum lag of 144 examining the relationship between hour and
production
PACF plot with a maximum lag of 20, examining relationship between hour - production
We found that while the residuals appeared roughly normally distributed, there were
signs of autocorrelation, indicating some temporal dependencies were not fully
captured. Additionally, we performed the Ljung-Box test, which confirmed significant
autocorrelation in the residuals.
Comparison of predicted and real production values over time for first approach,
indicating the presence of significant autocorrelation in the residuals as confirmed by
the Ljung-Box test
The model's performance was quantitatively assessed using ‘accu’ function, which were
compared to a baseline linear model. We will now include lagged values at 10 intervals,
as indicated by the peak in the PACF at lag 10. Although this model is impractical for
our forecasting task, we aim to evaluate its performance. The reason for its
impracticality is that we lack the necessary data for the lagged 10 value when predicting
future values (for example, the lagged 10 value for 03.01.2024 12:00 would be
02.01.2024 14:00, which we cannot know in advance). Nonetheless, we construct this
model to evaluate its performance.
Summary of performance metrics for the first model compared with the baseline linear
model
Second Approach : Linear Regression with Lasso Variables + Transformed Hour +
Lag 10:
In our second approach, we enhanced the initial model by including lag 10 values, as
indicated by the PACF plot. To do this, a new feature called prod_lag_10—which shows
the production value lag by 10 intervals. Then, using Lasso regression, we updated our
feature set to along with the previously chosen significant variables. After fitting the
linear regression model, we evaluated its performance by analyzing the residuals and
performing the Ljung-Box test.
Residuals plot , ACF of residuals , and histogram with density plot of residuals for the
second approach
Comparison of predicted and real production values over time for second approach
Summary of performance metrics for the second model compared with the previous
models
The results indicate that the model with lag 10 values improves accuracy, showing lower
RMSE and MAPE compared to both the Baseline-LM and Lasso(1sd)-LM models. This
analysis reveals that the underprediction issue is somewhat resolved in this model.
However, we agree that this model is not feasible because it is not practical to use lag
10 values in a real-time forecasting setting.This led us to develop a more practical
forecasting model using lag 24 and lag 36 values.
Third Approach : Linear Regression with Lasso Variables + Transformed Hour +
Lag 24+ Lag 36 (1sd):
In the third approach, we transformed the data to include lag 24 and lag 36 of the
production values. This means the model uses the production values from 24 and 36
hours before the current hour as predictors. We also transformed the hour variable to a
quadratic form: −(hour−12)2−(hour−12)2, ensuring the hour column peaks around noon
when solar production is typically highest. For feature selection, we identified the feature
columns and used them to create the predictor matrix XX and response vector yy. We
then fitted a linear regression model using these selected features.To evaluate the
model, we calculated various performance metrics and conducted residual analysis to
check for autocorrelation and normality.
Comparison of predicted and real production values over time for third approach
A very low p-value at Ljung-Box test (< 2.2e-16) suggests significant autocorrelation,
indicating that the model has not fully captured all temporal dependencies.
Residuals plot , ACF of residuals , and histogram with density plot of residuals for the
second approach
The residuals roughly follow a normal distribution but with some deviations, especially in
the tails. This suggests that while the model errors are somewhat normally distributed,
there may be some outliers or non-normality.
The ACF plot of residuals checks for autocorrelation, and there are significant spikes at
certain lags, indicating that the model has not fully accounted for temporal
dependencies in the data.
In the third model, we experienced an underprediction issue again. To determine which
variables are significant or not for the predictions in a linear regression model, the
p-values associated with the coefficients of each variable in the model summary are
typically examined. The model summary indicated that many variables were not
significant for the predictions. Based on that and the results of our tests indicating that
the model is insufficient, we will employ Lasso regression with a higher penalty
parameter when constructing our fourth model.
Summary of performance metrics for the third model compared with the previous
models
Fourth Approach : Linear Regression with Lasso Variables + Transformed Hour +
Lag 24+ Lag 36 (3sd):
As the fourth model, we built a time series linear regression model with Lasso variables,
which were acquired using a different lambda value. In this case, lambda was chosen
as the one within three standard deviations of the minimum MSE. Subsequently, as we
did in the previous approaches, we plotted the residual plots, performed the Ljung-Box
test, and compared its performance with the previous models.
Comparison of predicted and real production values over time for fourth approach
Residuals plot , ACF of residuals , and histogram with density plot of residuals for the
fourth approach
Summary of performance metrics for the fourth model compared with the previous
models
The presence of patterns in the residuals, significant autocorrelations, and deviations
from normality suggest that the model could be improved by addressing these issues.
As we see at the accuracy metrics, imposing a higher penalty unfortunately did not help
in reducing errors.
Using ggpairs, we examined each variable's link to production in more detail. We were
unable to identify an unmodeled association between the factors and the response
variable using ggpair plots. The ggpair graph of every variable appears to show very
little relationship. As a result, we now stop using linear regression models and switch to
ARIMA models.
Fifth Approach : ARIMA models for each hour:
In this approach, we start by grouping the data by hour. During the testing phase
created ARIMA models with auto.arima for every test day by iterating over the days.This
method allows us to update our ARIMA model daily with the latest available information.
For Hour 6:
Geom plot between date and production data for hour 6
The geom plot provides a clear visualization of the seasonal and daily variations in solar
power production for hour 6. We first did differencing on the non-stationary data before
building an ARIMA model. It is significant to highlight that using a 1-day difference is not
practical in our forecasting scenario because the most recent information available is
from 2 days prior.
Differenced production data over time for hour 6
ACF and PACF plots of differenced production data for hour 6
Predicted vs. actual production values for hour 6
For Hour 7:
Geom plot between date and differenced production data for hour 7
ACF and PACF plot of differenced production data for hour 7
Predicted vs. actual production values for hour 7
Summary of the simple ARIMA model for hour 7
Summary of fifth approach: To create separate ARIMA models for each hour, we
followed the same steps shown above for hours 6 and 7. For each hour, we first
examined the geom plot and ACF/PACF of our data to assess trends and stationarity.
We then applied differencing to remove trends and achieve stationarity, analyzed the
resulting plots, and compared the actual and predicted values. Then, we combined
these, and the outcomes were as follows:
Predicted vs. actual production values for unified all hours
Residuals plot , ACF of residuals , and histogram with density plot of residuals for fifth
model
Summary of performance metrics for the fifth model compared with the previous models
Sixth Approach : ARIMA for overall data: Finally, we attempted to create an ARIMA
model using all of our data.While doing this, we used the training set, and the results
were as follows:
Predicted vs. actual production values for fifth model
Predicted vs. actual production values for fifth model
Final Approach & Results:
Now that we have elaborated on all of our approaches in detail, let’s focus on the best
performing approach that we have developed. In the table below, the comparison of all
the developed approaches’ forecasting performances can be seen. In the table, it is
clearly seen that the 3rd approach (Linear Regression with Lasso Variables +
Transformed Hour + Lag 24+ Lag 36 (1sd) ) is the best performing approach in the
sense that it yields the most accurate forecasts.
Comparison of All Developed Approaches
In the table, we see that the final model performs the best. After determining the best
approach, we moved on with testing it. Our testing time horizon was 1st of February to
15th of May 2024. Between these dates, we tested our model by producing forecasts for
each date and comparing these forecasts to the actual realisations of solar power
production in these dates. This time, for the sake of a thorough testing, we also included
the hours of the day which we had previously determined as zero-production hours. In
the above table, it is seen that this model performed the best based on MAPE
comparison. More elaborative forecast results yielded by our final approach can be
visually seen in the figures below:
Our Final Approach Performance over the Test Period (February 1st - May 15th 2024)
Residual Analysis of Our Final Approach
Residual Analysis of Our Final Approach
In the residual analyses, we can examine our models in terms of the behaviour of its
residuals. We see that the residuals have a constant mean and variance, which is highly
required in a good time series model. In the second chart, residuals clearly show a
normal distribution pattern with no visible skew or autocorrelation. These findings
strengthen our belief in the accuracy of the final model, and show us that there is little to
no remaining unaccounted for information that is required for the model.
Conclusions:
In this study, we addressed the challenge of forecasting the hourly solar power
production at the Edikli Solar Power Plant in Niğde, Turkey. Given that solar energy
production is inherently dependent on meteorological factors, we aimed to develop a
model that leverages these variables to predict solar power generation accurately.Our
approach involved several stages. First, we organized our data in Python and applied a
general regression analysis. After this initial step, we decided to continue our work in R.
We then applied Lasso regression to select the most significant variables, refining our
feature set. We evaluated models with different sets of lagged values (Lag 10, Lag 24,
and Lag 36) and lambda values. Next, we developed ARIMA models for each hour and
an overall ARIMA model, accounting for temporal dependencies and seasonality. The
best-performing approach was a linear regression model with Lasso-selected variables,
a transformed hour, and lagged production values (Lag 24 and Lag 36). The resulting
model had the best performance metrics and showed the highest forecasting accuracy.
and thorough residual analysis showing no significant autocorrelation or non-normality.
In conclusion, our study highlights the importance of incorporating meteorological
variables, appropriate feature transformations, and lagged production values in
developing effective forecasting models for solar power production. The performance of
the final model underscores its potential for real-world applications in electricity pricing
and capacity planning, providing a valuable tool for optimizing operations at the Edikli
Solar Power Plant.
Future Work & Improvements:
Expanding the variable base would be a good improvement for our model. Although our
current variable data provide a solid foundation for our forecasts, a good additional
variable information would be the weather forecast for the solar power plant’s location.
By using this information, instead of using past weather condition data we can use
much more flexible and on point weather forecast data. This is especially essential in
today’s world, where the climate changes rapidly and each year shows more and more
extreme weather conditions. According to sector analyses, with the ongoing climate
change trend, the solar panels will be more and more valuable in terms of electricity
generation (Putol, 2024). Therefore, its impact on seasonality of production should be
considered as well, which may also lead to the creation of a new seasonal climate
change variable.
Links to the Project Codes:
R Codes:
https://github.com/BU-IE-360/spring24-kaanertan/blob/a01f703db374ee6f7597bac6e7b
b70b2ebb2d4b2/Project/IE360_Project_RCodes_Group28.ipynb
Python Codes:
https://github.com/BU-IE-360/spring24-kaanertan/blob/a01f703db374ee6f7597bac6e7b
b70b2ebb2d4b2/Project/IE360_Project_Data_processing_Group28.ipynb
References:
1. Adams, S. & Lambert, D. (2006). Earth Science: An Illustrated Guide to Science.
The Diagram Group.
2. Desonie, D. (2012). CK-12 Earth Science for High School. CK-12 Foundation.
Retrieved from:
https://archive.org/details/ost-earth-sciences-ck_12_earth_science_for_high_sch
ool/page/n1/mode/2up
3. Montgomery et al. (2008). Introduction to Time Series Analysis and Forecasting
4. Hyndman, R. J. & Athanasopoulos, G. (2018). Forecasting: Principles and
Practice
5. Putol, R. (2024). Climate change will increase the value of solar panels.
Earth.com.
https://www.earth.com/news/climate-change-will-increase-the-value-of-solar-pan
els/
